Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
Correct Answer
$6996
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5300 × 4% × 8
= $5300 ×4/100 × 8
= 5300 × 4 × 8/100
= 21200 × 8/100
= 169600/100
= $1696
Thus, Simple Interest = $1696
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1696
= $6996
Thus, Amount to be paid = $6996 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5300
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 4% × 8)
= $5300 + ($5300 ×4/100 × 8)
= $5300 + (5300 × 4 × 8/100)
= $5300 + (21200 × 8/100)
= $5300 + (169600/100)
= $5300 + $1696 = $6996
Thus, Amount (A) to be paid = $6996 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5300, the simple interest in 1 year
= 4/100 × 5300
= 4 × 5300/100
= 21200/100 = $212
Thus, simple interest for 1 year = $212
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $212 × 8 = $1696
Thus, Simple Interest (SI) = $1696
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1696
= $6996
Thus, Amount to be paid = $6996 Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.
(2) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(5) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.
(7) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.